CN101887585A - Method for calibrating camera based on non-coplanar characteristic point - Google Patents

Abstract

The invention discloses a method for calibrating a camera based on a non-coplanar characteristic point. The method comprises the following steps of: setting a three-dimensional target and establishing a three-dimensional target coordinate system, wherein the three-dimensional target can provide at least six non-coplanar characteristic points; shooting a three-dimensional target image by using a camera, wherein the shot image at least contains six non-coplanar characteristic points; extracting coordinates of the at least six non-coplanar characteristic points in the image coordinate system and solving a homography between the three-dimensional target coordinate system and the image coordinate system; solving an internal parameter and an external parameter of a camera according to the obtained homography; and carrying out non-linear optimization on the obtained internal parameter and the external parameter. The calibrating method provided by the invention has simple target setting, calibration completion just by shooting the image, flexible use method and higher calibrating precision.

Description

Camera marking method based on non-coplanar characteristic point

Technical field

The present invention relates to the camera calibration technology, be specifically related to a kind of camera marking method based on non-coplanar characteristic point.

Background technology

In recent years, utilize digital camera to carry out two dimension, three-dimensional reconstruction and size detection and obtained increasing utilization and research.Camera model has reflected the mapping relations of the plane of delineation and locus, and camera calibration is exactly an inner parameter and outside parameter of determining reflection camera optics and geometrical property.Wherein, camera intrinsic parameter is a preset parameter, does not change and changes along with camera position; What external parameters of cameras reflected is the position orientation relation of camera coordinate system and Reference coordinate system, and this parameter can change along with the variation of video camera pose.

The tradition scaling method is based on an accurate object calibrating block as the space object of reference, by setting up the scaling method that the corresponding relation between known point and its picture point on the object of reference calculates camera parameters.The tradition scaling method can be divided into the coplanar point demarcation according to the calibrating template kind and non-coplanar point is demarcated, and classical non-coplanar point scaling method has: DLT method, Tsai method, Chen Gang method, gorgeous method of summer etc.; The coplanar point scaling method has: Tsai method, Zhang Zhengyou method.

Tsai R Y. has provided a kind of two step standardizations based on radial constraint (RAC) in article " A versatile camera calibration technique for high accuracy 3D machine vision metrology using off the shelf TV cameras and lenses.R.Y.Tsai.; Robotics Automat 3; 1987; pp.323-344. ", this method utilizes coplane or non-coplane calibrating template to ask for camera interior and exterior parameter respectively simultaneously.This method can guarantee higher precision for distortion model, yet need demarcate in advance parameters such as picture centres.

During ZHANG Z Y. is at article " Flexible Camera Calibration by Viewing a Plane from Unknown Orientations.Zhengyou Zhang; Seventh International Conference on Computer Vision; 1999; Volume 1pp.666. " a kind of scaling method that uses the two dimensional surface target has more flexibly been proposed, this method is optimized the inside and outside parameter that obtains video camera by gathering the plane picture (at least 2) under the different unknown attitudes.

When video camera imaging plane and reference surface when parallel, the big even failure of camera parameters error of using the method for two dimensional surface target to calibrate.At this situation, some are suggested " Camera calibration with coplanar calibration board near parallel to the imaging plane. " (HongGen Luo LiMin Zhu and Han Ding in the method that video camera imaging plane and reference surface are used for camera calibration when parallel, Sensors and Actuators A:Physical Volume 132, Issue 2,20November 2006, Pages 480-486.).

ZHANG Z Y. is at article " Camera Calibration with one-dimensional objects[J] .IEEETransactions on Pattern Analysis and Machine Intelligence; 2004; 26 (7): 892-899. " in camera marking method based on the one dimension target has been proposed, though the processing of one dimension target is more or less freely, stated accuracy is high, but in calibration process, need an end of one dimension target is fixed, be difficult to when rotating in actual use guarantee the absolute fixing of stiff end, thereby influenced the precision of demarcating.

WU F C, HU Z Y, ZHU H J. article " Camera calibration with moving one-dimensional objects[J] .Pattern Recognition; 2005; 38 (5): 755-765 " in the scaling method that proposes based on plane motion one dimension target, though do not need one dimension target one end is fixed, in calibration process, need the support of motion platform.

People such as Chen Gang are at article " a kind of binocular vision sensor field calibration method based on three-dimensional template. " (Chen Gang, Che Rensheng, the optical precision engineering, 2004, a kind of method of using three-dimensional template to demarcate has been proposed 12 (6)), the Chen Gang method is not considered the influence of video camera imaging distortion, obtain one group of accurate image characteristic point and corresponding reference coordinate by three coordinate measuring machine, determine camera interior and exterior parameter by the linear transformation method, practicality is low, poor anti jamming capability and have bigger error.

People such as Zhang Guangjun have proposed a kind of plane target drone of several small sizes that uses and have formed the method that the flexible stereo target carries out camera calibration in Chinese invention patent " a kind of camera marking method based on flexible stereo target " (application number is 200810114607.7, and Granted publication number is CN100557635C).This scaling method is still the ZHANG Z Y. scaling method that uses the two dimensional surface target in itself, and this method further utilizes in the flexible target constraint independent of time that concerns on each sub-plane to optimize camera parameters.This method has certain applicability for the video camera of big visual field, still can't obtain the image of a plurality of planes target that comprises for the less video camera in visual field, and this method is also inapplicable.Further contemplate the plane target with the video camera imaging plane when parallel, ZHANG Z Y. scaling method can't calibrate the characteristics of correct camera parameters, the method for Zhang Guangjun should be noted that this problem when placing flexible target placement.The scaling method of Zhang Guangjun invention need make video camera relative to moving at least once with flexible target placement, can't move at some occasion video camera, and mobile flexible stereo target is difficult to guarantee that each sub-target relativeness is constant.

Summary of the invention

The objective of the invention is to overcome the deficiencies in the prior art, a kind of camera marking method based on non-coplanar characteristic point is provided, only need to take an image and can finish demarcation, and using method is flexible, stated accuracy is higher.

For achieving the above object, the present invention adopts following technical scheme:

A kind of camera marking method based on non-coplanar characteristic point is characterized in that, may further comprise the steps:

Steps A, stereo target is set, and sets up the stereo target coordinate system; Described stereo target can provide at least 6 non-coplanar characteristic points;

Step B, take the stereo target image, comprise 6 non-coplanar characteristic points in the captured image at least with video camera; Extract the coordinate of at least 6 non-coplanar characteristic points under image coordinate system, find the solution the homography matrix between stereo target coordinate system and the image coordinate system;

Step C, according to the homography matrix that step B obtains, find the solution the inner parameter and the external parameter of video camera.

Technique scheme is not considered the influence of video camera imaging distortion, may there be deviation in the video camera inside, the external parameter that obtain, be head it off, can introduce distortion, the inside, the external parameter that use Newton iteration method, Levenberg-Marquardt etc. that step C is obtained carry out nonlinear optimization.The present invention adopts the Levenberg-Marquardt nonlinear optimization method, that is: setting up with camera intrinsic parameter, outer parameter and the two rank radial distortion factors is parameter and the objective function that makes the projection error minimum, intrinsic parameters of the camera, the external parameter of trying to achieve with step C are initial value, utilize the Levenberg-Marquardt criterion to obtain the optimum solution of intrinsic parameters of the camera, external parameter.

The stereo target that uses in the technical solution of the present invention, can use two crossing plane target drones to form, also can use a plane target drone and one with its not the spatial point of coplane constitute, no matter which kind of constitutes, as long as satisfy at least 6 non-coplanar unique points is arranged on the target.

Description of drawings

Fig. 1 is the camera marking method process flow diagram that the present invention is based on non-coplanar characteristic point;

Fig. 2 is the synoptic diagram of specific embodiment of the invention neutral body target;

Fig. 3 a-e is respectively and tests photographic images in the specific embodiment of the invention.

Embodiment

Below in conjunction with accompanying drawing technical scheme of the present invention is elaborated:

As shown in Figure 1, the inventive method may further comprise the steps:

Steps A, stereo target is set, and sets up the stereo target coordinate system; Described stereo target can provide at least 6 non-coplanar characteristic points;

In this embodiment, for simplifying subsequent calculations, adopted stereo target as shown in Figure 2, this solid target is made up of two plane target drones that intersect vertically each other, 4 straight line parallels are arranged in the intersection of two plane target drones on each plane target drone, 9 straight lines are perpendicular to the intersection on plane, and every parallel lines spacing of closing on is 10mm, as unique point, then this stereo target can provide 81 unique points at most with intersection point between straight line.

Here represent the stereo target coordinate system with OXYZ, wherein the coordinate of each unique point under the stereo target coordinate system is expressed as P respectively ₁(x ₁y ₁z ₁) ... P _n(x _ny _nz _n), wherein n is the sum of selected characteristic point, n " 6.

Step B, take the stereo target image, comprise 6 non-coplanar characteristic points in the captured image at least with video camera; Extract the coordinate of at least 6 non-coplanar characteristic points under image coordinate system, find the solution the homography matrix between stereo target coordinate system and the image coordinate system; This step specifically comprises following each step:

Step Bl, take the stereo target image, comprise 6 non-coplanar characteristic points in the captured image at least with video camera; Extract the coordinate of at least 6 non-coplanar characteristic points under image coordinate system;

Step B2, use linear equation are found the solution homography matrix;

Note video camera imaging model is:

Wherein Represent three-dimensional target coordinate system coordinate,

Presentation video plane coordinate system coordinate; Ending is the camera intrinsic parameter matrix,

(u wherein ₀, y ₀) pixel coordinate of presentation video principal point, f _x, f _yRepresent respectively X, Y-axis to equivalent focal length, corpse is expressed as the picture plane inclination factor; [r ₁r ₂r ₃T] be the external parameters of cameras matrix, [r ₁r ₂r ₃] _{3 * 3}, t described respectively three-dimensional target coordinate system under camera coordinate system is described rotation and the relation of translation; S is scale factor arbitrarily.Homography matrix H=λ A[r ₁r ₂r ₃T], the note homography matrix

For the i of matrix H capable.

Consider scale factor s in the video camera imaging model, might as well make homography matrix element h ₄₃=1.Unique point p ₁(x ₁y ₁z ₁) correspondence image coordinate system coordinate is (u ₁v ₁), obtain unique point P successively _n(x _ny _nz _n) correspondence image coordinate system coordinate is (u _nv _n).

With unique point P ₁Bringing the video camera imaging model into has:

Cancellation accounts for and obtains system of equations:

Successively each unique point is brought in the camera model, until unique point P _nAnd obtain corresponding system of equations and be:

$\left\{\begin{array}{c}{x}_n{h}_{11}+y_n{h}_{21}+z_n{h}_{31}+h_{41}-x_n{u}_n{h}_{13}-y_n{u}_n{h}_{23}-z_n{u}_n{h}_{33}=u_n\\ x_n{h}_{12}+y_n{h}_{22}+z_n{h}_{32}+h_{42}-x_n{v}_n{h}_{13}-y_n{v}_n{h}_{23}-z_n{v}_n{h}_{33}=v_n\end{array}\right.$

From the above, n unique point obtains 2n equation altogether, and these equations are formed system of equations to be had:

$\left[\begin{array}{ccccccccccc}{x}_1& y_1& z_1& 1& 0& 0& 0& 0& -u_1{x}_1& -u_1{y}_1& -u_1{z}_1\\ 0& 0& 0& 0& x_1& y_1& z_1& 1& -v_1{x}_1& -v_1{y}_1& -v_1{z}_1\\ & & & & & .& & & & & \\ & & & & & .& & & & & \\ & & & & & .& & & & & \\ x_n& y_n& z_n& 1& 0& 0& 0& 0& -u_n{x}_n& -u_n{y}_n& -u_n{z}_n\\ 0& 0& 0& 0& x_n& y_n& z_n& 1& -v_n{x}_n& -v_n{y}_n& -v_n{z}_n\end{array}\right]X=\left[\begin{array}{c}{u}_1\\ v_1\\ .\\ .\\ .\\ u_n\\ v_n\end{array}\right]$

X=[h wherein ₁₁h ₂₁h ₃₁h ₄₁h ₁₂h ₂₂h ₃₂h ₄₂h ₁₃h ₂₃h ₃₃] ^T, note

$L_{2n\×11}=\left[\begin{array}{ccccccccccc}{x}_1& y_1& z_1& 1& 0& 0& 0& 0& -u_1{x}_1& -u_1{y}_1& -u_1{z}_1\\ 0& 0& 0& 0& x_1& y_1& z_1& 1& -v_1{x}_1& -v_1{y}_1& -v_1{z}_1\\ & & & & & .& & & & & \\ & & & & & .& & & & & \\ & & & & & .& & & & & \\ x_n& y_n& z_n& 1& 0& 0& 0& 0& -u_n{x}_n& -u_n{y}_n& -u_n{z}_n\\ 0& 0& 0& 0& x_n& y_n& z_n& 1& -v_n{x}_n& -v_n{y}_n& -v_n{z}_n\end{array}\right],$

Obviously when n 〉=6, there is unique solution in system of equations, and solution of equations is X=(L at this moment ^TL) ^-1L ^TK, thus homography matrix H obtained.

Can see that herein the video camera imaging model homography matrix of the inventive method is 3 * 4 matrixes, and the homography matrix in the Zhang Zhengyou method is 3 * 3 matrixes of this method homography matrix after degenerating.

Step B3, the homography matrix H that step B2 is obtained carry out nonlinear optimization;

In practice, owing to having noise in the process of obtaining picture point, make M and m can not satisfy linear equation.Suppose that picture point is subjected to independent distribution and average is that zero Gaussian noise is disturbed, so singly the optimum solution of reflecting property matrix H can be by making objective function

Minimum obtains, wherein m _i=(u _i, v _i), ${\hat{m}}_i=\frac{1}{{\stackrel{\‾}{h}}_3\·{\left[\begin{array}{cccc}{x}_i& y_i& z_i& 1\end{array}\right]}^T}\left[\begin{array}{c}{\stackrel{\‾}{h}}_1\·{\left[\begin{array}{cccc}{x}_i& y_i& z_i& 1\end{array}\right]}^T\\ {\stackrel{\‾}{h}}_2\·{\left[\begin{array}{cccc}{x}_i& y_i& z_i& 1\end{array}\right]}^T\end{array}\right];$

Homography matrix is found the solution problem and is converted into nonlinear optimal problem, use the Levenberg-Marquardt criterion to find the solution the optimum solution of homography matrix H, wherein the initial value of the required homography matrix H of L-M criterion uses the solving result of step B2, and parameter optimization uses data to be unique point P ₁P _nBut concrete grammar list of references " the The levenberg-marquardt algorithm; implementation and theory " (J.More that L-M optimizes, In G.A.Watson, editor, Numerical Analysis, Lecture Notes in Mathematics 630, Springer-Verlag, 1977).

Step C, according to the homography matrix that step B obtains, find the solution the inner parameter and the external parameter of video camera; Specifically comprise following each step:

Step C1, set up only relevant system of equations with camera intrinsic parameter according to the orthogonality of rotation matrix;

The homography matrix that calculates for non-coplanar characteristic point According to the video camera imaging model h is arranged ₁=λ Ar ₁h ₂=λ Ar ₂h ₃=λ Ar ₃h ₄=λ t, and consider r ₁, r ₂, r ₃There is equation in orthogonality $h_1^T{A}^{-T}{A}^{-1}{h}_2=0,$ $h_1^T{A}^{-T}{A}^{-1}{h}_3=0,$ $h_2^T{A}^{-T}{A}^{-1}{h}_3=0,$

$h_1^T{A}^{-T}{A}^{-1}{h}_1=h_2^T{A}^{-T}{A}^{-1}{h}_2=h_3^T{A}^{-T}{A}^{-1}{h}_3,$ Note $B=A^{-T}{A}^{-1}=\left[\begin{array}{ccc}{B}_{11}& B_{12}& B_{13}\\ B_{12}& B_{22}& B_{23}\\ B_{13}& B_{23}& B_{33}\end{array}\right],$ Define vectorial b=[B ₁₁B ₁₂B ₂₂B ₁₃B ₂₃B ₃₃] ^T, then can obtain following system of equations:

$\left[\begin{array}{c}{v}_{12}\\ v_{13}\\ v_{23}\\ v_{11}-v_{22}\\ v_{11}-v_{33}\end{array}\right]b=0$

Step C2, find the solution camera intrinsic parameter according to system of equations;

Supposing to gather the non-coplanar characteristic point image has m to open, and can obtain m homography matrix by step B, further according to step C1, then can obtain 5m equation, and remember that this system of equations is: Vb=0, wherein V is the matrix of 5m * 6.When m 〉=2, there is unique solution b; When m=1, make imaging plane inclination factor γ=0, promptly increase an equation of constraint [01000] b=0 to system of equations, then can be in the hope of solving b.As everyone knows, solution of equations b is a matrix V ^TV minimal eigenvalue characteristic of correspondence vector.Calculate matrix B by separating b, find the solution the camera intrinsic parameter matrix A according to formula in the ZHANG Z Y. scaling method, concrete solution procedure is referring to document " Flexible Camera Calibration by Viewing a Plane from Unknown Orientations " (Zhengyou Zhang, Seventh International Conference on Computer Vision, 1999, Volume 1pp.666), repeat no more herein.

Step C3, find the solution each outer parameter according to camera intrinsic parameter;

For the non-coplanar characteristic point image,, can obtain outer parameter matrix by the above-mentioned intrinsic parameter matrix A of finding the solution

$r_1=\frac{1}{\mathrm{\κ}}{A}^{-1}{h}_1,$ $r_2=\frac{1}{\mathrm{\κ}}{A}^{-1}{h}_2,$ $r_3=\frac{1}{\mathrm{\κ}}{A}^{-1}{h}_3,$ $t=\frac{1}{\mathrm{\κ}}{A}^{-1}{h}_4,$

Wherein, κ=1/A ^-1h ₁||=1/||A ^-1h ₂||=1/||A ^-1h ₃||;

To the matrix Q=[r that obtains ₁r ₂r ₃] carry out orthogonalization, according to ZHANG Z Y. scaling method, Singular Value Decomposition Using is Q=USV ^T, R=UV then ^TOuter parameter for its correspondence.Solution procedure is referring to document " Flexible Camera Calibration by Viewing a Plane from Unknown Orientations " (Zhengyou Zhang in detail, Seventh Intemational Conference on Computer Vision, 1999, Volume 1pp.666), repeat no more herein.

Step D, inner parameter and external parameter that step C is obtained carry out nonlinear optimization;

The present invention adopts the Levenberg-Marquardt nonlinear optimization method, that is: setting up with camera intrinsic parameter, outer parameter and the two rank radial distortion factors is parameter and the objective function that makes the projection error minimum, intrinsic parameters of the camera, the external parameter of trying to achieve with step C are initial value, utilize the Levenberg-Marquardt criterion to obtain the optimum solution of intrinsic parameters of the camera, external parameter; Particularly, in accordance with the following methods:

Suppose to gather m and open the reference substance image, get n calibration point on every image, and picture point is subjected to the Gaussian noise interference that average is zero independent distribution.By making the projection error objective function The minimum camera parameters of optimizing.

I opens j unique point P of image in function f _Ij, its image pixel coordinate figure is designated as m _Ij=(u _Ijv _Ij), corresponding target coordinate system coordinate is designated as M _Ij=(x _Ijy _Ijz _Ij), k ₁, k ₂Be respectively the single order second order distortion factor of introducing, A is a camera intrinsic parameter, [R _i, t _i] be the external parameters of cameras of i when opening image.I (m _Ij, A, k ₁, k ₂) be the normalized images coordinate system coordinate that goes out by the image pixel coordinate Calculation,

Be the normalized images coordinate system coordinate that calculates by object reference coordinate and outer parameter matrix.When optimizing, with rotation matrix R _iBe converted into pitching and roll (RPY) angle φ, θ, And with φ, θ,

Be optimized as parameter.

In the objective function According to camera model as can be known

$\hat{x}=[\left(u_{\mathrm{ij}}{-u}_0\right)-\mathrm{\γ}(v_{\mathrm{ij}}-v_0)/f_y]/f_x.$

$\hat{y}=(v_{\mathrm{ij}}-v_0)/f_y$

In the objective function (X wherein _CijY _CijZ _Cij) be a some P _IjCoordinate figure under camera coordinate system system has according to the video camera imaging model:

Non-linear minimizing uses the Levenberg-Marquardt criterion to find the solution.This criterion needs an initial value.Wherein the camera interior and exterior parameter initial value is the parameter value that calculates among the step C.Distortion factor k ₂, k ₂Initial value can find the solution by following linear method:

With unique point P _IjObtain in the substitution video camera imaging model:

Wherein $\begin{array}{c}\hat{x}=[(u_{\mathrm{ij}}-u_0)-\mathrm{\γ}(v_{\mathrm{ij}}-v_0)/f_y]/f_x\\ \hat{y}=(v_{\mathrm{ij}}-v_0)/f_y\end{array},\begin{array}{c}x=X_{\mathrm{cij}}/Z_{\mathrm{cij}}\\ y=Y_{\mathrm{cij}}/Z_{\mathrm{cij}}\end{array},{\left[\begin{array}{ccc}{X}_{\mathrm{cij}}& Y_{\mathrm{cij}}& Z_{\mathrm{cij}}\end{array}\right]}^T=\left[\begin{array}{cc}{R}_i& t_i\end{array}\right]\·\left[\begin{array}{c}{x}_{\mathrm{ij}}\\ y_{\mathrm{ij}}\\ z_{\mathrm{ij}}\\ 1\end{array}\right].$

Each unique point can obtain 2 equations as implied above as from the foregoing.With all unique point substitution video camera imaging models, a unique point can obtain 2mn equation, all equations is formed system of equations be designated as Mk=d, can obtain distortion factor initial value k=[k ₁k ₂(the M of] '= ^TM) ^-1M ^TD.

In order to verify the effect of scaling method of the present invention, compare according to following experimental technique and ZHANG Z Y. scaling method:

Experiment is the AVT Guppy F_033B video camera of 9mm with camera lens, and its image resolution ratio is 640 * 480; The stereo target that uses is printed the plane form by normal printer, is attached on cube iron block to obtain again; Take 5 of stereo target images at diverse location, sequence number is compiled and is 1-5, and each width of cloth image is shown in accompanying drawing 3a-3e; Adopt scaling method of the present invention and ZHANG Z Y. scaling method that above-mentioned video camera is demarcated respectively, compare two kinds of calibration values that scaling method obtains then; Because the external parameters of cameras data are huge, and general camera calibration mainly is in order to demarcate intrinsic parameter, so this experiment only compares the calibration value of camera intrinsic parameter.Consider that ZHANG Z Y. scaling method uses coplanar characteristic point to demarcate, choose one of them plane target drone that constitutes this stereo target when therefore testing and be used for carrying out the demarcation of ZHANG Z Y. method.

Experimental result is as follows, calibration result when wherein table 1 is only taken an image for using ZHANG Z Y. scaling method, calibration result when table 2 is only taken an image for using the inventive method, calibration result when table 3 is taken many images for using ZHANG ZY. scaling method, the calibration result when table 4 is taken many images for using the inventive method:

Table 1

Table 2

Table 3

Table 4

Can see from above experimental result, when using individual or less image, use non-coplanar point more more stable than the camera parameters that uses coplanar point to obtain; Along with the image usage quantity increases, use non-coplanar point and use coplanar point all to be tending towards obtaining a stable camera parameters.

In above-mentioned experiment, do not use high-precision calibrating piece or specific instrument, but use scaling method of the present invention finally still to obtain the result of a stable and degree of precision, further proved practicality of the present invention.In order further to improve the camera parameters precision, 3 can service precision higher dimension calibrating block or by along Z _wAxle plane of motion calibrating block fixed range obtains the higher non-coplanar characteristic point of positional precision.

Claims (3)

1. the camera marking method based on non-coplanar characteristic point is characterized in that, may further comprise the steps:

Steps A, stereo target is set, and sets up the stereo target coordinate system; Described stereo target can provide at least 6 non-coplanar characteristic points;

Step B, take the stereo target image, comprise 6 non-coplanar characteristic points in the captured image at least with video camera; Extract the coordinate of at least 6 non-coplanar characteristic points under image coordinate system, find the solution the homography matrix between stereo target coordinate system and the image coordinate system;

Step C, according to the homography matrix that step B obtains, find the solution the inner parameter and the external parameter of video camera.

2. according to claim 1 based on the camera marking method of non-coplanar characteristic point, it is characterized in that, also comprise step D behind the described step C: inner parameter and external parameter that step C is obtained carry out nonlinear optimization.

As described in the claim 2 based on the camera marking method of non-coplanar characteristic point, it is characterized in that, described nonlinear optimization is meant: setting up with camera intrinsic parameter, outer parameter and the two rank radial distortion factors is parameter and the objective function that makes the projection error minimum, intrinsic parameters of the camera, the external parameter of trying to achieve with step C are initial value, utilize the Levenberg-Marquardt criterion to obtain the optimum solution of intrinsic parameters of the camera, external parameter.

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